Rapid and precise quality control inspections of the soldering and assembly of electronic devices have become priority items in the electronics manufacturing industry. Many existing inspection systems for electronic devices and connections make use of penetrating radiation to form images which exhibit features representative of the internal structure of the devices and connections. These systems often utilize conventional radiographic techniques wherein the penetrating radiation comprises X-rays. Medical X-ray pictures of various parts of the human body, e.g., the chest, arms, legs, spine, etc., are perhaps the most familiar examples of conventional radiographic images. The images or pictures formed represent the X-ray shadow cast by an object being inspected when it is illuminated by a beam of X-rays. The X-ray shadow is detected and recorded by an X-ray sensitive material such as film or electronic means. Alternatively, tomographic techniques such as laminography and computed tomography (CT) may be used to produce cross-sectional images of the object being inspected. Laminography systems which are capable of achieving the speed and accuracy requirements necessary for electronics inspection are described in the following patents: 1) U.S. Pat. No. 4,926,452 entitled "AUTOMATED LAMINOGRAPHY SYSTEM FOR INSPECTION OF ELECTRONICS", issued to Baker et al.; 2) U.S. Pat. No. 5,097,492 entitled "AUTOMATED LAMINOGRAPHY SYSTEM FOR INSPECTION OF ELECTRONICS", issued to Baker et al.; 3) U.S. Pat. No. 5,081,656 entitled "AUTOMATED LAMINOGRAPHY SYSTEM FOR INSPECTION OF ELECTRONICS", issued to Baker et al.; 4) U.S. Pat. No. 5,291,535 entitled "METHOD AND APPARATUS FOR DETECTING EXCESS/INSUFFICIENT SOLDER DEFECTS", issued to Baker et al.; 5) U.S. Pat. No. 5,621,811 entitled "LEARNING METHOD AND APPARATUS FOR DETECTING AND CONTROLLING SOLDER DEFECTS", issued to Roder et al.; 6) U.S. Pat. No. 5,561,696 "METHOD & APPARATUS FOR INSPECTING ELECTRICAL CONNECTIONS", issued to Adams et al.; 7) U.S. Pat. No. 5,199,054 entitled "METHOD AND APPARATUS FOR HIGH RESOLUTION INSPECTION OF ELECTRONIC ITEMS", issued to Adams et al.; 8) U.S. Pat. No. 5,259,012 entitled "LAMINOGRAPHY SYSTEM AND METHOD WITH ELECTROMAGNETICALLY DIRECTED MULTIPATH RADIATION SOURCE", issued to Baker et al.; 9) U.S. Pat. No. 5,583,904 entitled "CONTINUOUS LINEAR SCAN LAMINOGRAPHY SYSTEM AND METHOD", issued to Adams; and 10) U.S. Pat. No. 5,687,209 entitled "AUTOMATIC WARP COMPENSATION FOR LAMINOGRAPHIC CIRCUIT BOARD INSPECTION", issued to Adams. The entirety of each of the above referenced patents is hereby incorporated herein by reference.
In automated X-ray inspection (AXI) of printed circuit assemblies, gray-scale images of interconnects or slices thereof are examined to detect and classify improper joints and/or to provide statistical process control data relating to the manufacturing process. For reasons including but not limited to portability, reproducibility and clarity, it is desirable that measurements taken relate directly to physical characteristics of the joint under inspection. In characterizing solder joints, for example, it is preferable to deal with measured joint thickness rather than gray scale pixel values. However, extracting solder thickness from the measured gray scale pixel values is complicated by several factors. First, X-ray sources used in AXI typically emit X-rays at many wavelengths with varying intensities as a function of wavelength. Additionally, in passing through a printed circuit assembly, X-rays will typically encounter other absorbers in addition to the solder, e.g., copper power and ground planes, tantalum capacitors, etc. Each material has its own characteristic absorption spectrum as a function of wavelength. The resulting interaction is highly non-linear, and complete characterization of the thickness of solder and other shading materials in the path is generally not possible from a limited number of gray scale calibration measurements.
Nonetheless, useful approximations can be made when prior knowledge of the assembly under inspection is available. For example, in many cases, solder thickness may be desired and it may be known that the background shading is due almost entirely to a particular material, e.g., copper. In such cases, by measuring background (due to the copper alone) and foreground (due to both copper and solder) gray values, one may attempt to estimate solder thickness if a suitable correction for background "shading" by copper can be constructed.
Previous calibration procedures have encountered a number of difficulties in practice. For example, previous attempts which use polynomial regression techniques to fit a set of calibration points to a surface which approximates solder thickness have been deficient. Such fitted surfaces frequently have unwanted maxima, minima, saddle points and inflection points, and often do not accurately reflect the underlying physical process. Better fits may be obtained by using a more constrained surface (e.g. one which is linear along one or more axis) to a portion of the calibration surface. This helps avoid the problems that often plague higher order regression surfaces, but leads to its own difficulties. In particular, multiple "patches" are often required to approximate the entire calibration surface. In the presence of measurement noise, this can lead to inconsistent behavior for points lying near the borders of adjacent patches.